1. Field of the Invention
The present invention relates to a digital filter, and, more particularly, to a digital band pass elliptic filter capable of changing the center frequency of a pass band and/or the pass band width.
2. Description of the Related Art
Digital band pass filters are used in various technical fields.
For example, Japanese Unexamined Patent Publication No. 16573/1980 discloses an infinite impulse response (IIR) variable digital filter which can independently alter the center frequency of its pass band and the width of the pass band.
The IIR variable digital filter described in this publication changes the center frequency and the pass band width in the following manner.
First, with P=j.OMEGA.=j2.pi.f, the transfer function H.sub.L (P) of a low-pass filter (LPF) on the P plane is expressed by an equation (1) below. EQU H.sub.L (P)=(a.sub.O P.sup.2 +a.sub.1 P+a.sub.2)/(P.sup.2 +b.sub.1 P+b.sub.2) (1)
The transfer function of the band pass filter can be obtained by transforming the transfer function H.sub.L (P) along the frequency axis according to the following equation (2). EQU P.fwdarw.B.sub.O (P+.OMEGA..sub.O.sup.2 /P) (2)
where B.sub.0 is the pass band width and .OMEGA..sub.O is the center frequency.
From the equations (1) and (2), the transfer function H.sub.B (P) of the band pass filter becomes as expressed by an equation (3). ##EQU1##
The transfer function on the Z plane, when acquired by the transformation given by the following equation (4), becomes as expressed by an equation (5) below. EQU P.fwdarw.(1-Z.sup.-2)/(2Z.sup.-1) (4) ##EQU2##
In the equation (5), .PHI.(Z, .OMEGA..sub.O.sup.2)/B.sub.0 is the function of the pass band width and center frequency of the filter. By acquiring .PHI.(Z, .OMEGA..sub.O.sup.2)/B.sub.0 from the desired (target) center frequency and the pass band width and substituting the result in the equation (5), the transfer function of the desired band pass filter can be obtained.
For the IIR variable digital filter disclosed in Japanese Unexamined Patent Publication No. 16573/1980, however, the value of the function .PHI.(Z, .OMEGA..sub.O.sup.2)/B.sub.0 should be obtained to alter the center frequency of the pass band and pass band width.
.PHI.(Z, .OMEGA..sub.O.sup.2)/B.sub.0 is a non-linear function of the center frequency and the pass band width and its computation is complex involving a vast amount of calculations, resulting in a long computation time and a large rounding error. Further, to store the transfer function and execute the computation, a large memory capacity is disadvantageously needed.